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Abstract

The end-to-end performance achieved by an adaptive optical (AO)
imaging system is determined by a combination of the residual
time-varying phase distortions associated with atmospheric turbulence
and the quasi-static unsensed and uncorrectable aberrations in the
optical system itself. Although the effects of these two errors on
the time-averaged Strehl ratio and the time-averaged optical transfer
function (OTF) of the AO system are not formally separable, such an
approximation is found to be accurate to within a few percent for a
range of representative residual wave-front errors. In these
calculations, we combined static optical system aberrations and
time-varying residual phase distortion characteristics of a deformable
mirror fitting error, wave-front sensor noise, and
anisoplanatism. The static aberrations consist of focus errors of
varying magnitudes as well as a combination of unsensed and
uncorrectable mirror figure errors derived from modeling by the Gemini
8-Meter Telescopes Project. The overall Strehl ratios and OTF’s
that are due to the combined effect of these error sources are well
approximated as products of separate factors for the static and
time-varying aberrations, as long as the overall Strehl ratio that is
due to both errors is greater than approximately 0.1. For lower
Strehl ratios, the products provide lower bounds on the actual values
of the Strehl ratio and the OTF. The speckle transfer function is
also well approximated by a product of two functions, but only where AO
compensation is sufficiently good that speckle imaging techniques are
usually not required.

References

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a NGS denotes a natural guide star, LGS is
an artifically generated laser guide star at range z, ψ is
the zenith angle, d is the width of a WFS subaperture,
r0 is the turbulence-induced atmospheric
coherence diameter, σθ is the rms WFS subaperture tilt
measurement accuracy, λ is the imaging wavelength, θ is the angular
offset between the guide star and the science object, and
θ0 is the isoplanatic angle. The notation
HV5/7 denotes the Hufnagel–Valley turbulence profile
scaled to yield r0 = 5 cm and
θ0 = 7 µrad at λ = 0.5
µm. Further description of these parameters is given in
the text.

Table 2

Strehl Ratio Results for Gemini-North Telescope and AO
System Parametersa

Phase Errors

Computation

Strehl Ratio (µm)

1.25

1.65

2.20

Turbulence

Exact

0.621

0.760

0.856

Typical aberrations

Exact

0.568

0.708

0.818

Best-case aberrations

Exact

0.762

0.852

0.913

Turbulence and typical aberrations

Exact

0.365

0.545

0.703

Multiplicative

0.353

0.538

0.700

Turblence and best-case aberrations

Exact

0.481

0.651

0.783

Multiplicative

0.473

0.648

0.782

a This table lists Strehl ratios computed
in three astronomical imaging bands based on the Gemini system
parameters listed in the last column of Table 1. The first section
of the table lists Strehl ratios computed separately for the effects of
atmospheric turbulence and optical system aberrations. The
remaining two sections of the table list Strehl ratios for the combined
effect of these two error sources, where the exact values were computed
using Eq. (2.7), and the multiplicative values were derived from
the first section of the table using approximation (2.9). The
multiplicative approximation is accurate to within a few percent over
the range of cases considered.

a NGS denotes a natural guide star, LGS is
an artifically generated laser guide star at range z, ψ is
the zenith angle, d is the width of a WFS subaperture,
r0 is the turbulence-induced atmospheric
coherence diameter, σθ is the rms WFS subaperture tilt
measurement accuracy, λ is the imaging wavelength, θ is the angular
offset between the guide star and the science object, and
θ0 is the isoplanatic angle. The notation
HV5/7 denotes the Hufnagel–Valley turbulence profile
scaled to yield r0 = 5 cm and
θ0 = 7 µrad at λ = 0.5
µm. Further description of these parameters is given in
the text.

Table 2

Strehl Ratio Results for Gemini-North Telescope and AO
System Parametersa

Phase Errors

Computation

Strehl Ratio (µm)

1.25

1.65

2.20

Turbulence

Exact

0.621

0.760

0.856

Typical aberrations

Exact

0.568

0.708

0.818

Best-case aberrations

Exact

0.762

0.852

0.913

Turbulence and typical aberrations

Exact

0.365

0.545

0.703

Multiplicative

0.353

0.538

0.700

Turblence and best-case aberrations

Exact

0.481

0.651

0.783

Multiplicative

0.473

0.648

0.782

a This table lists Strehl ratios computed
in three astronomical imaging bands based on the Gemini system
parameters listed in the last column of Table 1. The first section
of the table lists Strehl ratios computed separately for the effects of
atmospheric turbulence and optical system aberrations. The
remaining two sections of the table list Strehl ratios for the combined
effect of these two error sources, where the exact values were computed
using Eq. (2.7), and the multiplicative values were derived from
the first section of the table using approximation (2.9). The
multiplicative approximation is accurate to within a few percent over
the range of cases considered.